熵极小动力系统的复杂性

设X是一个紧致度量空间,f:X→X是一个连续映射,(X,f)是熵极小的.该文首先证明了f是强遍历的;另外,如果还假设X中存在f的一个真的(拟)弱几乎周期点,则得到f具有正拓扑熵且对任意的n1,f~n是遍历敏感依赖的.因此,f在Li-Yorke和Takens-Ruelle意义下是混沌的.该文所得结论改进和推广了最近的一些结论.     

小时滞梯度系统的动力学行为

该文研究下列具有小时滞的一般非线性梯度型发展方程_tu+Au=f(u(t),u(t-τ)).证明了当时间趋于无穷大时,时滞方程的每一个有界解将收敛于某一个平衡点,只要时滞足够小,这意味着时滞系统的行为非常类似非时滞系统.这里的方法主要是基于梯度系统不变集的Morse结构和发展方程的几何理论.这个结果的证明分两步完成:首先,在梯度系统和有限个孤立平衡点的假设下,证明了一定存在一个足够小的时滞使得时滞方程的任一个有界解将会最终进入并停留在某一个平衡点的邻域里面;其次,在双曲平衡点的假设下,运用指数二分性和一系列的估计,证明了一定存在ε0和足够小的τ0使得任一个落于某个平衡点ε-邻域内的解最终收敛于该平衡点,当时间趋于无穷大时.     

Thermal Behavior of Polypropylene-g-glycidyl Methacrylate Prepared by Melt Grafting

The thermal behaviors of glycidyl methacrylate (GMA)-grafted polypropylene (PP) (PP-g-GMA) with two different grafting degrees, namely, GPP1 and GPP2, were investigated by differential scanning calorimetry (DSC), polarized optical microscopy (POM), wide-angle X-ray diffraction (WAXD), dynamic mechanical analysis (DMA), and thermogravimetrical analysis (TGA). DSC results suggested that the GMA grafted PP exhibited higher crystallization temperature T_c, higher melting temperature T_m, and higher crystallinity compared with the neat PP. The isothermal crystallization kinetics was analyzed with the Avrami equation and the total crystallization activation energy was calculated. It was concluded that the crystallization processes of PP and the grafted PP were controlled by nucleation and the values of the crystallization activation energy of PP and the grafted PP were almost identical. POM results suggested that the GMA grafted PP exhibited smaller spherulites size compared with the neat PP. WAXD patterns indicated that the neat PP encouraged the formation of γ phase, compared with the grafted PP, during the crystallization process. DMA results showed that melt grafting did not induce a clear effect on the γ-transition and β-transition of the amorphous phase but resulted in a decrease in mobility of the PP chains in the crystals. TGA curves suggested that the melt grafting slightly improved the thermal stability of PP.     

一个奇摄动微分方程非线性混合边值问题

研究了一个三阶半线性微分方程的奇摄动非线性混合边值问题.利用边界层函数法构造了该问题的形式渐近解,并采用微分不等式理论证明了解的存在性,给出了渐近解的误差估计,最后得出了边界层函数指数型衰减的结论.     

二维分数阶Volterra积分方程的修正block-by-block方法

基于经典block-by-block方法的思想,构造了二维分数阶Volterra积分方程的一个修正block-by-block数值求解格式.该方法的优点在于只需求解u(x1,y),u(x2,y),u(x,y_1)和u(x,y_2),其他未知量均不需要耦合求解.数值算例表明该格式具有较好的逼近性.     

环状硅酸盐图的友好指数集

Let G be a graph with vertex set V(G) and edge set E(G). A labeling f : V(G) →Z2 induces an edge labeling f*: E(G) → Z2 defined by f*(xy) = f(x) + f(y), for each edge xy ∈ E(G). For i ∈ Z2, let vf(i) = |{v ∈ V(G) : f(v) = i}| and ef(i) = |{e ∈ E(G) : f*(e) =i}|. A labeling f of a graph G is said to be friendly if |vf(0)- vf(1)| ≤ 1. The friendly index set of the graph G, denoted FI(G), is defined as {|ef(0)- ef(1)|: the vertex labeling f is friendly}. This is a generalization of graph cordiality. We investigate the friendly index sets of cyclic silicates CS(n, m).     

A surface plasmon resonance imaging system for the stimulated living cell analysis

In this paper, a surface plasmon resonance imaging(SPRI) system for cell analysis is developed for obtaining the surface plasmon resonance(SPR) signal from the interactions between cells and different stimuli. The system is constructed with a red laser light source, a P-polarizer, a glass prism, a 5× objective lens, a charge coupled device(CCD) camera, a gold sensor chip, a polydimethylsiloxane(PDMS) reaction well and a mechanical scanning device. The system is applied to mapping living cells in response to stimuli by characterization of the refractive index(RI) changes. Cell responses to K+ in KCl solutions with concentrations of 5 mmol/L, 20 mmol/L, 50 mmol/L and 100 mmol/L are collected, which indicates that the SPRI method can distinguish the concentration of the stimuli. Furthermore, cell responses to epidermal growth factor(EGF) and vascular endothelial growth factor(VEGF) are studied independently. The binding of EGF receptor(EGFR) and EGF is collected as the first signal, and the internal change in cells is recorded as the second signal. The cell response to VEGF is different from that to EGF, which indicates that the SPRI as a label-free, real-time, fast and quantitative method has a potential to distinguish the cell responses to different stimuli.     

TMT tertiary mirror axis calibration with laser tracker

A novel fiber Bragg grating(FBG)displacement sensor is proposed,which can achieve wide measuring range displacement detection with variable measurement precision due to its mechanical transfer structure of helical bevel gear.A prototype is designed and fabricated.The maximum detection displacement of this prototype is 1.751 m,and the precision grade changes from 0.2%to 6.7%.Through analyzing the experiment data which is obtained in the calibration experiment,the measuring range of this sensor is from 0 m to 1.532 m,and the wavelength shift errors between experiment data and theory calculation are all less than 5%.     

Dual-core photonic crystal fiber polarization splitter based on lead silicate glass

Integral imaging is a three dimensional(3D)display technology without any additional equipment.A new system is proposed in this paper which consists of the elemental images of real images in real mode(RIRM)and the ones of virtual images in real mode(VIRM).The real images in real mode are the same as the conventional integral images.The virtual images in real mode are obtained by changing the coordinates of the corresponding points in elemental images which can be reconstructed by the lens array in virtual space.In order to reduce the spot size of the reconstructed images,the diffuser in conventional integral imaging is given up in the proposed method.Then the spot size is nearly1/20 of that in the conventional system.And an optical integral imaging system is constructed to confirm that our proposed method opens a new way for the application of the passive 3D display technology.     

全光纤高速模拟信号偏振态测量系统的研究

全光纤高速偏振态测量,尤其是模拟信号的偏振态高速测量在光纤通信和光纤传感等领域中有着重要应用。在深入研究光电探测器放大电路的基础上,搭建了基于光纤偏振控制器(PC)、偏振分束器(PBS)以及模拟光电探测器的全光纤高速偏振态测量系统。用搭建的系统对0~50 MHz模拟信号的偏振态进行了测量,并与商用偏振分析仪进行了误差比较。实验表明,此偏振态测量系统可实现速率0~50 MHz模拟信号Stokes参量的准确测量,显示在邦加球上的测量误差半径在0.03以下,与商用偏振分析仪处于同一量级。系统重复性良好,且可测模拟信号的速率远超目前商用偏振分析仪,为许多待测光为模拟信号的光纤传感系统提供了有效的测量手段。